摘要:

A method is proposed to eliminate trends from a sample from a non-stationary system of linear stochastic difference equations. The auto-covariance matrix and the spectral density matrix of the detrended component of the sample are derived. The latter matrix turns out to have the same form as the spectral density matrix for a stationary system when expressed in terms of the roots of the system. Since the parameters of the system are assumed known throughout the paper, the problem of statistical inference does not arise.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500995

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

An approximation, based on the sum of independent uniform random variables, to the Wilcoxon-Mann-Whitney null-distribution, is proposed. Numerical comparisons with the normal approximation show that this uniform approximation is appreciably more accurate even when the smaller sample size is large. A table of percentiles of the distributions of the sum of independent uniform random variables is given for the uniform approximation. An extension of existing tables of percentiles of the exact distribution is also given.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500996

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500997

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A method is proposed for deriving an estimation procedure from the recurrence relationship between probabilities in a discrete distribution. It is limited to cases in which only one parameter occurs in the recurrence relationship. To find a confidence interval for the parameter we consider the estimating function obtained and this may be shown to be dependent on differences between the cumulative probability function and its estimated value.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500998

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10500999

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A Bayesian approach to the estimation of the parameters of a two-parameter exponential distribution and the reliability function associated with it is developed using censored samples. Bayesian point estimates are obtained for these three quantities and it is shown that under a suitable choice of the prior distribution and of the loss function they are approximately equivalent to the corresponding maximum likelihood estimates (MLE) and minimum variance unbiased estimates (MVUE). Also, Bayesian probability points and confidence points are obtained for both the parameters and their approximate equivalence is brought out.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501000

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

If experimental data have been analyzed using a logarithmic transformation of the actual observations, taking the antilog of the mean of the transformed variables yields a biased estimate of the mean μ of the original variable. To obtain an unbiased estimate of this mean a correction for bias must be applied. The table at the end of this note provides values of a function of the sample size and variance of data transformed to logarithms to base 10 which, when added to the mean of the transformed data, yields an unbiased estimate of the mean of the original variable after transforming back. This estimate is more efficient than the mean of the untransformed observations.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501001

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Lett1andt12be two independent normally distributed random variables with zero means and equal variances, each divided by a common estimate of the standard deviations. The joint distribution oft1,t2is a bivariate Studentt-distribution. The integral of the joint frequency function over certain types of critical regions in the (t1,t2)-plane may be written as the linear combination of two definite integrals which are easy to compute. Critical values for five alternative hypotheses in simultaneous tests ont1andt2are presented, and approximations which are asymptotically exact are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501002

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Approximations good to nine decimal places, in terms of the shifted Chebyshev polynomials, are given for Mills' Ratio over two pairs of ranges, [0, 1], [1, ∞] and [0, 2], [2, ∞]. It is shown how to derive polynomial approximations which give comparable accuracy.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501003

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

LetZ1,Z2be two independent, identically distributed random variables whose logarithms are normally distributed. We derive the generating function, expectation, and variance of the logarithm of the sum ofZ1andZ2. The expressions for the expectation and variance involve the sums of rapidly converging series. Converging upper and lower bounds to the expectation are given to indicate the number of terms in the series that need to be evaluated to yield a specified number of significant places.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501004

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor